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This paper investigates non-binary low-density parity-check (LDPC) erasure correcting codes suitable to guarantee reliable transmission in wireless communications systems. In particular, irregular repeat-accumulate (IRA) codes are considered, characterized by linear-time encoding complexity. The performance of non-binary IRA codes is compared with their binary counterparts on the packet erasure channel (PEC), with considerable advantages for the non-binary construction. Particularly, it is illustrated that the performance of short-block-length erasure correcting IRA codes over Galois fields (GFs) of order q >; 2 approaches, under maximum-likelihood (ML) decoding, the performance of ideal maximum distance separable (MDS) codes. This is especially appealing in the context of satellite communications, where efficient codes are required to cope with small link margins.